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Comparison of y-scaling for electrons and hadrons. R. J. (Jerry) Peterson University of Colorado USA

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Comparison of y-scaling for electrons and hadrons

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comparison of y scaling for electrons and hadrons
Comparison of y-scaling for electrons and hadrons

R. J. (Jerry) Peterson

University of Colorado USA

Much has been learned from inclusive electron scattering from nuclei at intermediate energies and momentum transfers. Scaling, with several variables condensed into just one, has served to unify many efforts. Electron-nuclear physics goes by a very well-known reaction mechanism. Although the strong interaction complicates analysis of inclusive hadron scattering at similar energied and momentum transfers, there is much to be learned from the data available.

Today—rules, constraints and a few examples for (p,px), (p,nx), (p,px), (p,p0x) and (K+,K+x).



One and only one elastic collision between the beam particle and a bound nucleon, for “billiard ball” kinematics. Thus, combine q and w data to a single scaling variable=y today.

In-medium elastic cross sections are known from free space scattering, with known off-shell effects.

The number of one-and-only-one collisions can be computed with the eikonalGlauber model, which depends upon in-medium total beam-nucleon cross sections. Trivial for electrons.

Copy the lessons learned from electron scaling for the hard case of hadronquasifree scattering.


This is interesting because we can probe the interactions among nucleons within the nucleus by quasifree scattering from one of them while it is interacting, but need to match the quantum numbers of the probe and the interaction.

scaling of the second kind

Scaling of the Second Kind

For electron charge scattering, the response is independent of A. Is this true for hadrons?

We need Aeff or Neff for computing F(y), so this is a test of our Glauber method. We force this scaling by changing the in-medium beam-nucleon total cross section, with ratio b of in-medium/free total cross sections =0.70-0.75

superscaling both first and second kinds
Superscaling, both first and second kinds
  • Include the expected nucleon Fermi momentum by plotting

Y = y / kFermi

f(Y) = F(y) x kFermi

scaling of the first kind

Scaling of the First Kind

The one-and-only-one scattering is tested by being independent of momentum transfer q, as found for electron scattering, but not obvious for hadrons.

scattering of the third kind

Scattering of the Third Kind

Are the responses for carbon near q=550 MeV/c the same for ALL hadrons? Another test of the Glauber method.

  • 1. Hadron scattering can meet the conditions for quasifree scattering, and thus can sense in-medium beam-hadron single-interactions, as shown by scaling of the First Kind, best for light nuclei.
  • 2. We can count the nucleons struck elastically once and only once by the Glauber method, if smaller in-medium total cross sections are used, giving scaling of the Second and Third Kinds.
  • 3. The isospin responses of nuclei can be separated with hadrons, and are not the same.
  • 4. At the special beam momentum of 750 MeV/c, pion SCX can separate transverse spin responses.